Absorption spectra of high-redshift quasars suggest that the reionization of cosmic hydrogen was complete near z∼ 6. The dominant sources of ionizing photons responsible for this reionization are generally thought to be stars and quasars. In this paper we make a quantitative estimate of the relative contributions made by these sources. Our approach is to compute the evolution of the post-overlap ionizing background radiation by combining semi-analytic descriptions of reionization in a clumpy medium with a model for the quasar luminosity function. Our overall model has two free parameters, the star formation efficiency and the minimum quasar luminosity. By adjusting these parameters, we constrain the relative contributions made by stars and quasars through comparison with reported observations. We find that the relative quasar contribution (at z= 5.7) to the ionizing background was between 1.4 and 14.5 per cent. The range of uncertainty is dominated by the unknown minimum quasar luminosity.